Conditional Probability Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
Two cards are drawn without replacement from a standard deck. Given that the first card is a king, what is the probability the second card is also a king?

Solution

  1. 1
    After drawing one king, there are 33 kings remaining out of 5151 cards.
  2. 2
    P(2nd king∣1st king)=351=117P(\text{2nd king} \mid \text{1st king}) = \frac{3}{51} = \frac{1}{17}.

Answer

P=117P = \frac{1}{17}
Without replacement, the sample space shrinks after each draw. The conditional probability accounts for the updated deck composition.

About Conditional Probability

The conditional probability P(A∣B)P(A|B) is the probability of event AA occurring given that event BB has already occurred.

Learn more about Conditional Probability →

More Conditional Probability Examples

Example 1 medium

In a class of [formula] students, [formula] play soccer, [formula] play basketball, and [formula] pl

Example 2 hard

A test for a disease is [formula] accurate (true positive rate) with a [formula] false positive rate

Example 4 hard

A jar contains [formula] red marbles and [formula] blue marbles. Two marbles are drawn without repla

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